A THEORY OF SPIN DYNAMICS IN THE CLASSICAL 2-DIMENSIONAL HEISENBERG MAGNET

The wavevector-dependent spin autocorrelation function of a classical Heisenberg model on a square lattice is calculated from the coupled-mode theory of spin dynamics. This theory is consistent with the spherical model for static spin correlations; as the temperature, T, approaches zero the inverse correlation length kappa approximately exp(-const/T). For a ferromagnetic exchange coupling, the decay rate of long wavelength fluctuations, GAMMA(q), is proportionnal to q2T1/2 in the limit (q/kappa) --> infinity, whereas in the opposite, hydrodynamic limit GAMMA(q) is-proportional-to q2{T ln(kappa/q)}1/2. At the wavevector for incipient antiferromagnetic ordering, the decay rate is proportional to kappaT1/2, while the corresponding decay rate near the Brillouin zone centre is proportional to (q2T1/2/kappa). The coupled-mode equations for ferromagnetically and antiferromagnetically coupled models are solved numerically on a fine grid of wavevectors. The spin autocorrelation function, and its power spectrum, are surveyed over a wide range of temperatures and wavevectors.